The linear ZF detection is a vital technology to offer low complexity and implementation cost for IoT communications[1]}, [2]}. Hence, we assume that the received signal is reconstructed by using a ZF detector. Specifically, the ZF estimate of the transmitted symbol streams at cluster \(k\)  can be obtained by multiplying \({\bf y}_k\)  with \(({\sqrt{\ell (d_k)}}{{{{\bf {H}}_k}{\bf {V}}} })^\dag \)  as
\({\bf {\hat{s}}} &= {\bf {s}} + \frac{1}{\sqrt{\ell (d_k)}}\left({{{{\bf {H}}_k}{\bf {V}}} }\right)^\dag {{\bf {n}}_k}.\) 
